{
  "_public_export": {
    "status": "RIEMANN HYPOTHESIS OPEN",
    "record_type": "SANITIZED_HISTORICAL_SOURCE_SNAPSHOT",
    "source_path": "research/full_ground_capture/state.json",
    "source_sha256": "8905c11ad1eaa7dd83f1ef89714c8dae133ed3b13cfb9d798a9845967df5d4e9",
    "exported_on": "2026-09-30",
    "public_credit": "@ykbballer91",
    "license": "CC-BY-4.0",
    "ai_assisted": true,
    "original_fields_are_historical": true,
    "checks_rerun_in_public_export": false,
    "scope": "Historical claims and verification records retain their original scope. Priority 1 cyclicity is even L2 only; full-ground capture and RH remain open.",
    "references": {}
  },
  "date": "2026-09-30",
  "track": "FULL-GROUND CAPTURE / CYCLIC RADICAL HIERARCHY",
  "current_deliverable": "Priority 1: cyclicity only",
  "rh_status": "OPEN",
  "cyclicity_status": "PROVED",
  "conclusion": "K IS CYCLIC IN EVEN L2: PROVED",
  "fourier_convention": "hat f(x) = integral_R f(t) exp(-ixt) dt; hat k = Xi/4; Xi(x)=xi(1/2+ix)",
  "measure": "dmu(x)=|Xi(x)|^2 dx",
  "all_absolute_moments_finite": true,
  "positive_exponential_moments": "integral exp(b|x|) dmu < infinity for every 0 < b < pi/2",
  "moment_asymptotic_proved": true,
  "moment_asymptotic": "m_2n = sqrt(2pi) Gamma(v) (pi/2)^(-v) [digamma(v)+2 gamma-log(pi^2)+o(1)], v=2n+9/2",
  "moment_asymptotic_extra_input": "Unconditional zeta mean-square error O(T^(5/12)); Simonic-Starichkova arXiv:2105.06821v3",
  "carleman_divergence_proved": true,
  "carleman_requires_sharp_moment_asymptotic": false,
  "carleman_summand_asymptotic": "m_2n^(-1/(2n)) ~ pi e/(4n)",
  "hamburger_determinate": true,
  "all_polynomials_dense_in_full_weighted_L2": true,
  "even_polynomials_dense_in_even_weighted_L2": true,
  "even_polynomials_dense_in_full_weighted_L2": false,
  "direct_exponential_moment_density_proof_included": true,
  "Xi_multiplier_is_onto_isometry": true,
  "even_derivative_family_cyclic_in_even_L2": true,
  "RH_used": false,
  "zero_simplicity_used": false,
  "novelty_claimed": false,
  "proof_method": "Analytic proof, primary-source theorem audit, independent adversarial review; no machine formalization",
  "finite_head_spanning_status": "NOT_STARTED",
  "conditioning_status": "NOT_STARTED",
  "growing_m_constants_status": "NOT_STARTED",
  "full_even_ground_capture_status": "NOT_PROVED_NOT_STARTED",
  "parity_comparison_status": "NOT_STARTED",
  "form_core_property_proved": false,
  "G_star_proved": false,
  "rh_closed": false,
  "merged_into_existing_proof_graph": false,
  "next_action": "Report Priority 1 only. Any subsequent Priority 2 must separately establish finite-head conditioning; density alone is not ground capture."
}